Question

We would like to form a 7-member committee, consisting of 3 faculty members and 4 students. There are 40 faculty members and 300 students. How many different ways can we form the committee?

Answer 1

The number of combinations of the 40 faculty members taken 3 at a time is:
\[\large C(40, 3)=\frac{40!}{3!(40-3)!}\]
The number of combinations of the 300 students taken 4 at a time is:
\[\large C(300, 4)=\frac{300!}{4!(300-4)!}\]
Each of the combinations of faculty members can be taken with each of the combinations of students. Therefore the total number of possible combinations is given by:
\[\large C(40, 3) \times C(300, 4)=you\ can\ calculate\]